Question

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm. If 1 cm³ of molasses has mass about 1.2 g, find the mass of molasses that can be poured into each mould.
(class 10 CBSE SAMPLE PAPER 2017-18 MATHS)

Answer 1

SOLUTION:

Given, mould is in the shape of a frustum of a cone in which r2= 30/2, r1=35/2 cm, h= 14 cm.

Quantity (volume) molasses that can be poured into it= volume of the frustum

= π/3 × h (r1² + r2²+r1r2)
= 1/3×(22/7) × 14 [(35/2)²+(30/2)²+(35/2 × 30/2]
= 44/3[ 306.25 + 225 +262.5]
= 44/3 × 793.75= 11641.7 cm³

Given : 1 cm³ of molasses = 1.2 g

Mass of the  molasses that can be poured into  each mould= 11641.7 × 1 2 = 13970.04 g= 13970.04/1000=  13.97 kg

[ 1g = 1/1000 kg]

Hence, Mass of the  molasses that can be poured into  each mould=  13.97 kg= 14 kg (approx)


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Answer 2

ANSWER
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Volume of frustum is given by V


= 13πh(r21+r22+r1r2), 


Hence the height is given as 28cm, r2 = 70cm and r1 = 60cm


V = (1/3)*3.14 *28 ( 602 + 702 + 60 *70) = 372194.66cm3



If 1cm3 = 2.4gram


So 372194.66cm3 = 372194.66* 2.4 = 893267.2 gram = 893.267 kg



So the mass of molasses is 893.267Kg


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